Royal Society (Great Britain).

The Philosophical transactions of the Royal society of London, from their commencement in 1665, in the year 1800 (Volume 8) online

. (page 17 of 85)
Online LibraryRoyal Society (Great Britain)The Philosophical transactions of the Royal society of London, from their commencement in 1665, in the year 1800 (Volume 8) → online text (page 17 of 85)
Font size
QR-code for this ebook


thinks it has at present ; so that it might have been reduced to that which it
now has, by the diurnal motion on its axis, &c. But Dr. Desaguliers, who is
of Sir Isaac's opinion, has made appear, in the Philos. Trans. N" 388, that M.
Mairan's supposition is contrary to the laws of motion ; and has moreover pro-
posed several considerable doubts on the observations and suppositions employed
by M. Cassini, in his determination of the earth's figure in 17 18.

As soon as the meridian of Paris had been extended from one sea to the
other, and M. Cassini had thence deduced a confirmation of the system of the
earth's being longer at the poles ; M. De Lisle imagined a new method of de-
ciding the question, viz. by the observation of the degrees of the parallel, com-
pared with those of the meridian. For that purpose he considered, that as the
degrees of the meridian and those of the parallel, at the same elevation of the
pole, had different relations, according to the different figures ascribed to the
earth ; nothing more was requisite for concluding which hypothesis was the
true one, than to determine this relation by immediate observation.

Having supposed, that there had been observed on the parallel of Paris, a
space nearly of the saine magnitude with that on the meridian, that is, of about
13 degrees, since that on the meridian is about 84^ degrees ; he found by an
exact calculation, that according to the figure which M. Cassini has given to
the earth, this space ought to contain 13^ of the parallel, more than in the
hypothesis of the earth's being spherical ; which appeared considerable enough
to decide between these two hypotheses, and by a stronger reason between the
hypotheses of Newton and Cassini, seeing the difference ought to be still more
considerable than that now specified.

He concluded, at least, that, independent of the figure of the whole earth
which could not be determined by the sole observations made in France, with-
out making suppositions, and admitting principles, which are still liable to be
contested ; it would be of great consequence towards constructing exact charts
of the kingdom, to ascertain this relation by observations, which consisted only
in forming triangles along the parallel of Paris, and observing at the two ends
the difference of the meridians, by the most exact methods. This difference
seemed to be so considerable, that he was in hopes of being able to determine
it by means only of two places within sight of each other, and situated to the east
and west; provided their difference of longitude were accurately observed, in-
dependently of astronomical observations, by means of lighted fires ; after the
manner that M. Picart put in practice in Denmark, for determining the difl^er-



128 PHILOSOPHICAL TRANSACTIONS. [aNNO 1737.

ence of longitude of the astronomical tower at Copenhagen and of Uraniburg
in the Isle of Huen. With this intent, in the month of April 1720, M. De
Lisle went some distance from Paris southward, to the places which he judged
most proper for the purpose ; but his design was not then executed, for want
of assistance, and for other reasons, which he passes in silence. Since that
time, he found that the Marquis Poleni had hit upon the same thought ; as
may be seen in his letter to the Abbot Grandi, dated in November 1724.

The decision of this famous question, of the figure of the earth, had stopped
there, when in the year 1733, the minister of France having thought it neces-
sary to construct an exact map of the whole kingdom ; and being informed,
that the work could not be better carried on, than by the astronomers of the
Royal Academy of Sciences, applied to M. Cassini on that head ; who was of
opinion, that, to execute it with the utmost exactitude, the same method ought
to be employed as for the meridian, by taking through the whole extent of the
kingdom, triangles connected by means of objects seen successively, one from
another, &c. This project of making a map of France by such triangles, had
been already offered to M. Colbert, by Mons. Picart, in 168], but was not
then executed. However, M. Cassini proposed, that these triangles should be
begun in a direction perpendicular to the meridian ; in order to render these
operations of service towards the decision of the earth's figure, pursuant to the
method spoken of above : and M. Cassini, having in person undertaken these
operations, and having carried them that same year, 1733, from Paris to St.
Malo, whose longitude from Paris M. Picart had observed in 168I ; the rela-
tions of the degrees on the meridian and parallel, were found to be such as
were required in the hypothesis of the earth lengthened at the poles, and even
more lengthened than Cassini had determined in 17I8. For instead of the
diminution of a 6oth part for each degree of the parallel, which M. De Lisle
had found according to the earth's figure, as determined by Cassini in 17 18, he
deduced from his operations in 1733, a diminution of the 36th part of each
degree.

It is true, that M. Cassini, in the account he gave of this determination at
the public meeting of November 14, 1733, does not give it as entirely certain;
because the longitude of St. Malo, with regard to Paris, was collected from one
observation only of Jupiter's first satellite, in which there may possibly be some
error : but at least M. Cassini seems certain, that there is a very considerable
diminution in the degrees of the parallel of Paris, which confirms his opinion
of the earth's being longest at the poles. This we are likely to have a better
assurance of hereafter, as we are informed that this measurement of the parallel
of Paris, is carrying on in France by M. Cassini's sons, M. Maraldi's nephew.



VOL. XL.] PHILOSOPHICAL TUANSACTIONS. 120

and several other young mathematicians, instructed by M. Cassini in this sort
of work.

M. De Lisle has already said, that all these operations performed in France,
for the figure and magnitude of the earth, could not serve to determine the
earth's figure out of Frnnce, without the assistance of certain hypotheses ;
unless the same thing were undertaken and carried on in the other regions of
tlie earth, more northern and southern than France. It was on this considera-
tion, that the Royal Academy of Sciences took up the resolution of sending some
astronomers to make the like observations as near the equator and the poles as
possible, which are the places where the difference of the degrees on the meri-
dian ought to be the greatest, according to the different hypotheses.

In the month of April 1735, three mathen)aticians and astronomers of the
academy, viz. Messieurs Godin, Bougher, and De la Condamine, set out from
France for the province of Quito, the most northern part of Peru in America;
to observe, just under the equinoctial line, the magnitude of some degrees of
the meridian and equator.

As to the other mathematicians and astronomers of the same academy, viz.
Messieurs de Maupertuis, Camus, Clairaut, and Monnier, who were sent to
the north, they departed from France in April 1730, with Mr. Celsius, pro-
fessor of astronomy at Upsal, who accompanied them to Sweden, as far as the
bottom of the gulph of Bothnia, where they might measure about a degree on
the meridian at its crossing the polar circle. But as they had not finished their
operations, it is not yet known whether the magnitude of the degree measured
by them, favours the opinion of M. Cassini, or that of Sir Isaac Newton. All
we know is, that they have found the length of the simple pendulum favourable
to the latter, that is, longer under the polar circle than farther south. De la
Croyere had already found the same thing : for being at Archangel in 1728, he
there observed, in the most exact manner he possibly could, the length of the
simple pendulum, which he found to be -^ parts of a line longer than at Paris.

We are likewise informed by the other astronomers gone to Peru, that in
their way towards the equator, being at St. Domingo, in the latitude of 18°
37', they there found the pendulum swinging seconds, to be about 2 lines
shorter than at Paris. Thus, all we as yet know from those gentlemen, on the
expeditions to the north and the line, confirms the opinion of Sir Isaac Newton
and his adherents : and yet M. Mairan pretends, that this shortening of the
pendulum towards the equator, is in one sense entirely independent of the
earth's figure.

Thus it appears from the foregoing account, that the question concerning the
earth's figure is not yet at an end. Nay, it is not impossible, that after finish-

VOL. VIIJ. S



130 PHILOSOPHICAL TRANSACTIONS. [aNNO 1737.

ing all the observations which are actually making, new difficulties may arise,
and new objections be started, that may prevent its being entirely decided.
However, all this work cannot fail giving great light to this important question,
and procuring considerable advantages to geography, astronomy, and natural
philosophy.

It is with this view, and particularly to render such important service to the
geography of Russia, that M. De Lisle thinks it necessary to undertake a work
of that nature in Russia ; towards executing which they have great advantages
which other nations have not. One of the principal of these advantages, is the
great extent of Russia every way. For were the meridian of the imperial ob-
servatory of Petersburg to be determined, it might be carried to between 22
and 13 degrees ; which is a fourth part of the distance from the pole to the
equator. The meridians of Mosco and Astracan are not of less extent ; and
consequently we might, by the measurement of some one of these meridians, de-
termine more exactly, than could have hitherto been done, the inequality that
subsists between the degrees of the meridian.

This is what the great Cassini wished, when, after having, in the year 1701,
determined this inequality by the extent of 7 degrees observed in France, as has
been mentioned above, he says, that this fact might be verified by measurations
of greater extent, if the other princes of the earth would contribute as much
as the King of France, towards the perfecting of sciences.

In the great extent which might be given to the meridian of Petersburg,
there would be the advantage of knowing, by operations connected together, or
uninterrupted, the magnitude of some degrees equal to those which have been
measured in France, and to that which the French astronomers have measured
in Sweden ; and not only all the degrees between the two, which the French
astronomers have not had in their power to observe, but also some degrees
farther northward than that measured by them in Sweden.

As the exigencies of geography require the triangles, taken for the determi-
nation of the meridian, to be continued on every side, and principally in direc-
tions perpendicular to the meridian, or according to the parallels ; with how
great exactness may we not then determine the proportion of the degrees on the
parallels to those on the meridian, by means of the vast extent of the Russian
empire, which on its western side extending as far as all the dominions of
Europe from the most northern to the most southern, has no other bounds to
the east than the east itself, so to speak ; seeing its extent that way contains
near half the earth ?

Another great advantage to be obtained by the work now proposed to be
made in Russia, is, that, coming after others, we shall reap the benefit of all



VOL. XL.] PHILOSOPHICAL TRANSACTIONS. 131

their knowledge and experience in the like kind of measureinenls : whence we
may expect to succeed and execute it better than could have been done else-
where, by appl)ing timely remedies against the difficulties that occurred in
other places.

These operations are to be founded on a basis of the greatest length possible;
which must be actually measured, and with the greatest exactness ; as it is to
serve for a foundation to the measurement of all the triangles. And in this
point too there is a very great convenience near Petersburg, seeing on the ice,
we may measure out a basis, greater than has been hitherto taken, namely,
from the coast of Ingria about Peterhoff, to the coast of Finland toward Syster-
beck. There is not less than 20 wersts distance between these two extremities,
and this great distance may be measured very exactly, the ice being very even.
And as this basis is situated between the Isle of Cronstad and Petersburg, in a
direction nearly perpendicular to the distance from Petersburg to Cronstad ;
there can be no better method for inferring thence, by exact observation of the
angles taken at the extremities of this basis, the distance from the centre of the
imperial observatory, to the steeple of the new church at Cronstad; which two
objects are seen reciprocally from each other, and are not less than 30 wersts
asunder : and this distance, onee known exactly, will serve as a foundation for
all the triangles to be taken ; of which each of the sides may have not less than
from 30 to 40 wersts, according as objects are found advantageously situated
for that purpose. It should begin with the mountain of DouderhofF. which,
with the imperial observatory, and the steeple of Cronstad church, forms one
of the most convenient triangles imaginable for the subject proposed.

In taking observations at these three places, it must then be tried to discover
others of the same advantageous situation ; but when no remarkable objects are
found of the desired situation and distance, they must be erected on purpose, in
the same manner as in other countries. The most necessary instruments for
executing this undertaking, are, besides the ordinary astronomical instruments,
a common quadrant of between 2 and 3 feet radius, for observing the angles of
the triangles ; and a portion of a circle of the greatest radius that can be con-
veniently had, for observing the arches of the heavens corresponding with the
distances measured on the earth. As to the instrument for observing the arches
of the heavens, its radius ought not to be less than from 12 to 15 feet : but it
is not necessary that it should contain a large portion of a circle. It is only re-
quisite to have this portion somewhat larger than the arch of the heavens in-
tended to be measured. Thus, as the meridians, which may be traced in Russia,
can be extended only between 22 and 23 degrees, it will suffice that the instru-
ment employed, be a portion of a circle of 30 degrees

s 2



132 PHILOSOPHICAL TRANSACTIONS. [aNNO 1737-

M. Picart, for his first operation, got an arch of a circle made of 18 degrees
and of 10 feet radius, with which he thought himseU' sure within 2 or 3 seconds:
and no other instrument was used in the chief observations for the meridian of
Paris. The astronomers who are gone to America, carried with them an in-
strument of 12 feet radius, and of a portion of a circle of 30 degrees. But
those come to Sweden, contented themselves with a portion of a circle of 54-
degrees, and 9 feet radius: but this instrument, made by Mr. George Graham,
a very able English mechanician, is by its construction so exact, that the
astronomers who have used it, think, themselves certain to 2 seconds. The one
wanted for the observations in Russia, ought to be made by the same artist,
and of the same construction.

It is with such an instrument that Mr. Bradley, a celebrated English astro-
nomer, has discovered, in the meridian altitudes of some fixed stars, certain
constant and annual variations, which do not proceed either from the variation
of the refractions, or from the parallax of these stars, or from any nutation or
wavering of the earth's axis ; but which he accounts for by the successive mo-
tion of light. Whatever be the cause of these variations, as they may possibly
happen in the space of time requisite to be spent in making the observations for
the meridian, or in passing from one end of the meridian to- the other; it is
necessary, with the same instrument, or such another, that is of pretty near
the same exactness, to examine the variations of the stars made use of: it
would therefore be of considerable advantage, not only for the observations of
the measurement of the earth, but also for all the other principal researches in
astronomy, to have orders given for procuring two mural quadrants of Mr.
Graham's make, and of the same construction, as already specified; for which
there are walls already raised at the imperial observatory, in the plane of the
meridian. With these two quadrants, which might be of 7 feet radius, and the
moveable telescope 9 or 10 feet long, we should be in a condition to make ob-
servations of the utmost accuracy, such as the present state of astronomy
requires.

Besides these instruments now mentioned, which are of absolute necessity to
a solid establishment of astronomy and geography in this country, there are still
some other smaller instruments, that may be of great use in the operations, or
may serve to make other curious and useful observations at the same time, that
those for the measurement of the earth are making.

When the sides of the triangles, taken for measuring the earth, terminate at
very elevated places, as on the tops of the highest mountains, it is necessary to
reduce these triangles to what they would be, had they been observed in hori.
zontal planes on a level with the sea. For this purpose, we must know the



VOL. XL.] PHILOSOPHICAL TRANSACTIONS. 133

height of the mountains above the sea's level, which cannot always be deter-
mined geometrically, or would at least be too tedious to perform : therefore, in
the meridian of Paris, which crossed very high mountains, M. Cassini was of
opinion, that he ought to fix their height by a shorter method, which is that of
the height of the simple barometer, observed on the top of each mountain,
and compnred with that observed at the same time in another place, whose
elevation above the sea's level was known. But as that method supposes the
knowledge of the proportion which the different fallings of the mercury keep
with the different heights to which the barometer is carried ; and as natural
philosophers are not as yet entirely agreed on this head, for want of observa-
tions of sufficient accuracy ; thence it happened, that Dr. Desaguliers, making
it appear that M. Cassini has not employed the most exact proportion, found
reasons for correcting, or at least for doubting, of some of M. Cassini's calcu-
lations. Thus it must be by the assistance of new experiments, better circum-
stanced than those hitherto made, and pursuant to a theory entirely agreeing
with these experiments, that this method may be employed with certainty, for
determining the height of mountains by the barometer, and reducing the
angles observed from the tops of these high places, to what they would be, if
they had been observed on a plane at the level of the sea. Now these new ob-
servations can be made on our way in tracing the meridian ; and for that pur-
pose M. De Lisle began to construct compound barometers, which being very
nice, will serve to observe with accuracy, the quantity of the mercury's fall, at
the different elevations to which they shall be carried, to fix with greater
certainty the proportion of that fall.

There is still another method of determining the elevation above the level of
the sea of all the points, in which the triangles terminate, that are made for
the measurement of the earth. This may be done by beginning these opera-
tions near the sea, and actually measuring how many toises and feet the places
of the first stations are elevated above the level of the sea. For if the angles of
the apparent elevations of the second stations, seen from the first, be after-
wards observed, it will be an easy matter, from the known distances, to deduce
the true elevations of the latter above the former, and consequently above the
sea's level, making proper allowances in the calculations for the difference of
the apparent level from the true one. In this method, nothing is to be appre-
hended but the variation of refractions ; but for this a remedy may be found,
for the most part, by returning again, that is, by reciprocally observing the first
stations seen from the second : for if it be found, that as much as the second
station appears elevated above the first, so much the first is depressed below the



134 PHILOSOPHICAL TRANSACTIONS. [aNNO J 737.

second, except the small difference which must arise according to the given
distance, it will be a proof, that the refraction has been of no prejudice.

The other considerable observations and experiments, to be made in the
journies undertaken for such inquiries, are, the observations of the magnetic
needle, both as to its dip and variation : but chiefly the observations of the
length of the simple pendulum, which at present is become requisite to be ob-
served with as much exactness, and in as many places, as is possible; but also
for which there are new methods invented, which probably surpass those hither-
to made use of; in as much as, since those methods have been found by the
the Royal Academy of Sciences of Paris, it was thought proper to notify them
to the astronomers sent to Peru, to put them in practice in their observations.

The actual Mensuration of the Basis proposed in the preceding Article. By M.

De Lisle. N° 445, p. 50.

M. De Lisle undertook to measure the basis mentioned above, and had the
good fortune to measure it very exactly on the ice, by taking the precise distance
between the castle of Peterhoft', and the castle of Doubki, opposite to it, on
the coast of Finland. He found the distance between the opposite walls of
these castles to be 74,250 feet English. This basis, being much greater than
any of those employed hitherto for this purpose, gives room to expect great
exactness in the whole work, when it shall be carried on in the same manner.
It will at the same time serve to make a very exact map of the bottom of the
gulph of Finland. It is for the same design, and for better ordering the charts
of the coasts of the Baltic, that he intended (as soon as my project shall be ap-
proved here in its full extent) to begin to measure my triangles along the coasts
of Ingria and Livonia, to the islands of Dagho, Oesel, &c. And that the
charts of the places taken in by these triangles may be finished at the same time,
he designed to take with him all the charts of these parts, which could be had
to verify and correct them in his way.

He likewise intended to publish, as soon as possible, all the operations and
observations made in the expedition; that thus early benefit may be reaped from
them, and that the public, at the same time the charts come out, may be ac-
quainted with the foundation on which they are constructed.

Observations of two Parhelia, or Mock-Suns, seen Dec. 30, 1735; and of an
Aurora Borealis, Dec. 11, 1735. By the Rev. Timothy Neve. N''445, p. 52.

On Tuesday, Dec. 30, J 735, between Cherry Orton and Alwalton, in the



VOL. XL.] PHILOSOPHICAL TRANSACTIONS. 135

coutity of Huntingdon, Mr. Neve observed two parhelia, the first of which
shone so bright, that at first sight he took, it for the real sun, till looking a little
farther on his left hand, he was convinced of the mistake, by seeing the true
sun much the brightest in the middle, and a mock-sun on each side, in a line
exactly parallel to the horizon. He guessed their distance to be about 40 dia-
meters of the sun, or, as they usually appear, 23 degrees. That on the left
hand of the sun, when he saw it first, was small and faint, but in about 2 mi-
nutes time it became as large and bright as the other, and appeared at once as
two white lucid spots on each side the sun, east and west, seemingly as large,
but not so well defined : in about 3 minutes they lost both their colour and
form, and put on those of the rainbow ; the red and yellow in both very
beautiful and strong nearest to the sun, the other colours fainter. They became
as two parts of an arch, or segment of a circle, with the concave towards the
sun, only round at top, the light and colours streaming downwards, and tend-"
ing towards a point below. This continued for about 4 or 5 minutes, when the
colours gradually disappearing, they became as before, two lucid spots, with-
out any distinction of colours. They lasted a full hour, sometimes one brighter,
and sometimes the other, according to the variation of the clouds and air, as
he supposed. When he first saw it, it was exactly a quarter after eleven. There
had been a frost in the morning, which went away pretty soon, with a thick



Online LibraryRoyal Society (Great Britain)The Philosophical transactions of the Royal society of London, from their commencement in 1665, in the year 1800 (Volume 8) → online text (page 17 of 85)